In the beginning most law enforcement badges were star shaped. For example here are two star shaped badges, one from the city of Milwaukee and one from Milwaukee County, both date from the late nineteenth century. Then around the turn of the century shield shaped badges became the new style and here again are two examples from Milwaukee city and county. As the 20th century progressed most cities stayed with the shield shaped designs while most county sheriffs departments returned to the star shaped badges as illustrated here again with two more examples from Milwaukee city and county. My guess would be that since the star shaped badges are the oldest and most sheriff departments predate the municipal police departments the majority of the sheriffs departments went back to the star badges. I will post this in General (Multi-Cat.) for lack of a law enforcement or police category.